Factorized Duality, Stationary Product Measures and Generating Functions

Factorized Duality, Stationary Product Measures and Generating Functions

Redig, F.H.J. (TU Delft Applied Probability)
Sau, F. (TU Delft Applied Probability)

2018

We find all self-duality functions of the form (Formula presented.)for a class of interacting particle systems. We call these duality functions of simple factorized form. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion processes, as well as duality and self-duality functions for their continuous counterparts. The approach is based on, firstly, a general relation between factorized duality functions and stationary product measures and, secondly, an intertwining relation provided by generating functions. For the interacting particle systems, these self-duality and duality functions turn out to be generalizations of those previously obtained in Giardinà et al. (J Stat Phys 135:25–55, 2009) and, more recently, in Franceschini and Giardinà (Preprint, arXiv:1701.09115, 2016) . Thus, we discover that only these two families of dualities cover all possible cases. Moreover, the same method discloses all simple factorized self-duality functions for interacting diffusion systems such as the Brownian energy process, where both the process and its dual are in continuous variables.

Duality
Generating function
Interacting particle systems
Intertwining
Orthogonal polynomials

http://resolver.tudelft.nl/uuid:2a53f54d-6457-450c-882c-8b020275e78d

https://doi.org/10.1007/s10955-018-2090-1

0022-4715

Journal of Statistical Physics, 172 (4), 980-1008

Institutional Repository

journal article

© 2018 F.H.J. Redig, F. Sau